Adaptive multiresolution finite element method based on second generation wavelets

Finite Elements in Analysis and Design

Volumn 43, Issue 6-7, 2007, Pages 566-579

  He, Yumin ^a   Chen, Xuefeng ^a   Xiang, Jiawei ^a   He, Zhengjia ^b  

^a XI'AN JIAOTONG UNIVERSITY   (China)

^b XI'AN JIAOTONG UNIVERSITY   (China)

Author keywords

Adaptive algorithm; Finite element method; Multiresolution analysis; Second generation wavelets

Indexed keywords

ADAPTIVE ALGORITHMS; APPROXIMATION THEORY; FINITE ELEMENT METHOD; MULTIRESOLUTION ANALYSIS; STIFFNESS MATRIX;

SCALE-DECOUPLING WAVELET; SECOND GENERATION WAVELETS; WAVELET VANISHING MOMENTS;

WAVELET TRANSFORMS;

EID: 33947232713     PISSN: 0168874X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.finel.2006.12.009     Document Type: Article

References (23)

1. Mallat S.G. A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans. Pattern Anal. Machine Intel. 11 (1989) 674-693
2. Spanos P.D., Ravi V., and Rao S. Random field representation in a biorthogonal wavelet basis. ASCE J. Eng. Mech. 127 2 (2001) 194-205
3. Harbrecht H., Paiva F., Pérez C., and Schneider R. Biorthogonal wavelet approximation for the coupling of FEM-BEM. Numer. Math. 92 (2002) 325-356
4. Kaminski M. Homogenization-based finite element analysis of unidirectional composites by classical and multiresolutional techniques. Comput. Methods Appl. Mech. Eng. 194 (2005) 2147-2173
5. Ko J., Kurdila A.J., and Pilant M.S. A class of finite element methods based on orthonormal, compactly supported wavelets. Comput. Mech. 16 (1995) 235-244
6. Ma J.X., Xue J.J., Yang S.J., and He Z.J. A study of the construction and application of a Daubechies wavelet-based beam element. Finite Elem. Anal. Des. 39 (2003) 965-975
7. Chen X.F., Yang S.J., Ma J.X., and He Z.J. The construction of wavelet finite element and its application. Finite Elem. Anal. Des. 40 (2004) 541-554
8. Sweldens W. The lifting scheme: a construction of second generation wavelets. SIAM J. Math. Anal. 29 2 (1997) 511-546
9. Sweldens W. The lifting scheme: a custom-design construction of biorthogonal wavelets. Appl. Comput. Harmonic Anal. 3 2 (1996) 186-200
10. W. Sweldens, P. Schröder, Building your own wavelets at home, Wavelets in Computer Graphics, ACM SIGGRAPH Course Notes, 1996, pp. 15-87.
11. Ercelebi E. Second generation wavelet transform-based pitch period estimation and voiced/unvoiced decision for speech signals. Appl. Acoust. 64 (2003) 25-41
12. Yserentant H. On the multilevel splitting of finite element spaces. Numer. Math. 49 (1986) 379-412
13. Yserentant H. Hierarchical bases. In: O'Malley R.E. (Ed). Proceedings ICIAM 91 (1992), SIAM, Philadelphia 256-276
14. Amaratunga K., and Sudarshan R. Multiresolution modeling with operator-customized wavelets derived from finite elements. Comput. Methods Appl. Mech. Eng. 195 (2006) 2509-2532
15. Vasilyev O.V., and Kevlahan N.K.-R. An adaptive multilevel wavelet collocation method for elliptic problems. J. Comput. Phys. 206 (2005) 412-431
16. Castrillón-Candàs J., and Amaratunga K. Spatially adapted multiwavelets and sparse representation of integral equations on general geometries. SIAM J. Sci. Comput. 24 5 (2003) 1530-1566
17. R. Sudarshan, S. D'Heedene, K. Amaratunga, A multiresolution finite element method using second generation Hermite multiwavelets, Second MIT Conference on Computational Fluid and Solid Mechanics, 2003, pp. 1-6.
18. D'Heedene S., Amaratunga K., and Castrillón-Candás J. Generalized hierarchical bases: a Wavelet-Ritz-Galerkin framework for Lagrangian FEM. Eng. Comput.: Int. J. Computer-Aided Eng. Software 22 1 (2005) 15-37
19. Sudarshan R., Amaratunga K., and Grätsch T. A combined approach for goal-oriented error estimation and adaptivity using operator-customized finite element wavelets. Int. J. Numer. Meth. Eng. 66 (2006) 1002-1035
20. Deslauriers G., and Dubuc S. Interpolation dyadique, in Fractals, dimensions non entiéres et applications (1987), Masson, Paris pp. 44-55
21. Deslauriers G., and Dubuc S. Symmetric iterative interpolation processes. Constr. Approx. 5 (1989) 49-68
22. Mallat S. A Wavelet Tour of Signal Processing (2003), China Machine Press, Beijing, China
23. Barinka A., Barsch T., Charton P., et al. Adaptively wavelet schemes for elliptic problems-implementation and numerical experiments. SIAM J. Sci. Comput. 23 3 (2001) 910-939